Theorems · Theorem · linear algebra
LinearMap.sum_single_apply
∀ {ι : Type x} (φ : ι → Type i) [inst : (i : ι) → AddCommMonoid (φ i)] [inst_1 : Fintype ι] [inst_2 : DecidableEq ι]
(v : (i : ι) → φ i), ∑ i, Pi.single i (v i) = v- Defined in
- Mathlib.LinearAlgebra.Pi
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommMonoidstatement and proof · cited by 12,281
- Fintypestatement and proof · cited by 7,736
- Finset.sumstatement · cited by 5,195
- Finset.univstatement and proof · cited by 3,473
- Pi.singlestatement and proof · cited by 518
- Finset.sum_applyproof · cited by 234
- Finset.sum_pi_singleproof · cited by 8
Cited by3
Results whose statement or proof uses this declaration.
- ContinuousLinearMap.sum_comp_singleproof · cited by 4
- ProbabilityTheory.HasGaussianLaw.iIndepFun_of_covariance_strongDualproof · cited by 3
- ProbabilityTheory.iIndepFun.hasGaussianLawproof · cited by 3